2.1 Data

2.2 Anchoring Metrics

We start by constructing four country-specific metrics aimed at capturing the extent of anchoring of inflation expectations at horizon h over a given period ω:

• Metric #1 – Deviation of long-term mean inflation forecasts from target. If inflation expectations are well anchored, beliefs about future inflation should be, on average, close to the inflation target pursued by the monetary authority (Demertzis et al., 2012; Kumar et al., 2015). The root-mean-square deviation of the mean inflation forecast at horizon h from the inflation target over period ω is given by

  $\begin{array}{cc}\sqrt{\frac{1}{T}\underset{t=1}{\overset{T}{\mathrm{\Sigma }}}({\pi }_t^{e,h}-{\pi }_t^{*}{)}^2},withh=3,\mathrm{...},7;t\in \omega & \left(1\right)\end{array}$

  in which π* is the central bank’s inflation target for inflation-targeting economies or the one-year moving average of 10-year-ahead inflation forecasts $\left({\pi }_t^{e,10}\right)$ otherwise.

• Metric #2 – Variability of mean long-term inflation forecasts. If inflation expectations are well anchored, revisions of agents’ long-term forecasts should be small, and thus the average forecast relatively stable over time (ibid.). The standard deviation of the mean inflation forecast at horizon h over period ω is given by

  $\begin{array}{cc}\sqrt{\frac{1}{T-1}\underset{t=1}{\overset{T}{\mathrm{\Sigma }}}({\pi }_t^{e,h}-\overline{{\pi }^{e,h}}{)}^2},withh=3,\mathrm{...},7;t\in \omega & \left(2\right)\end{array}$

  in which $\overline{{\pi }^{e,h}}$ is the average of mean inflation forecasts over period ω.

• Metric #3 – Dispersion of long-term inflation forecasts. Individual beliefs about long-term inflation should be close to each other if expectations are well-anchored—and would coincide if they are perfectly anchored (Capistrán and Ramos-Francia, 2010; Dovern et al., 2012; Ehrmann, 2015; Kumar et al., 2015). The dispersion of forecasts is captured by the standard deviation of h-year-ahead inflation forecasts of individual forecasters at each period t, averaged over period ω:

  $\begin{array}{cc}\frac{1}{T}\underset{t=1}{\overset{T}{\mathrm{\Sigma }}}\left[\sqrt{\frac{1}{J-1}\underset{j=1}{\overset{J}{\mathrm{\Sigma }}}({\pi }_{j,t}^{e,h}-{\pi }_t^{e,h}{)}^2}\right],withh=3,\mathrm{...},7;t\in \omega & \left(3\right)\end{array}$

  in which ${\pi }_{j,t}^{e,h}$ denotes the inflation forecast of forecaster j at time t for horizon h and ${\pi }_t^{e,h}$ is the average across forecasters.

• Metric #4 – Sensitivity of long-term inflation forecasts to inflation surprises. Under well-anchored expectations, there should be little comovement between long-term inflation expectations and short-term inflation expectations, which would capture inflation surprises (Ehrmann, 2015; Kumar et al., 2015). The sensitivity of h-year-ahead inflation forecasts to short-term forecasts, β^h, is obtained by estimating the following country-specific regressions over period ω:

  $\begin{array}{cc}\mathrm{\Delta }{\pi }_t^{e,h}=\alpha +{\beta }^h\mathrm{\Delta }{\pi }_t^{e,1}+{ϵ}_t,withh=3,\mathrm{...},7;t\in \omega & \left(4\right)\end{array}$

  in which $\mathrm{\Delta }{\pi }_t^{e,1}and\mathrm{\Delta }{\pi }_t^{e,h}$ denote the change in mean inflation forecasts for the short term (that is, for the current year) and for h years ahead, respectively, between surveys at t — 1 and t.

These measures are computed for each forecast horizon from three- to seven-year-ahead inflation forecasts. While Metric #1 and Metric #3 can be computed for each period t in which a survey is available, a minimum number of surveys is needed to compute Metric #2 and Metric #4. In the analysis that follows, we set those minimum numbers of surveys at 4 and 10, respectively. Annex Figure A.2 shows the cross-country distribution of anchoring based on three-year-ahead inflation expectations for a balanced panel of economies with data available since 1998.

The four metrics we propose are complementary, with advantages and shortcomings—including in terms of data coverage—and no single metric may fully capture the extent of anchoring. For instance, if long-term expectations are well-coordinated and stable around a level above the central bank’s objective and do not react to short-term inflation surprises, one may argue that the economy has a strong nominal anchor. This would be reflected in relatively good readings in Metric #2 through Metric #4, although Metric #1 would score relatively bad. Similarly, if long-term expectations are stable around the target on average, but there is substantial disagreement across individual forecasters, the good reading in Metric #1, Metric #2, and Metric #4 would stand in contrast with a bad score under Metric #3.

3.1 Terms-of-Trade Shocks

A common challenge for analyzing empirically the effect of variations in the terms of trade is to identify exogenous shocks. Standard measures of terms of trade—the overall export-to-import price ratio—are affected by price rigidities and incomplete pass-through, making identification almost impossible (Chen and Rogoff, 2003). We follow an approach often adopted in the literature (Aizenman et al., 2012; Ricci et al., 2013; Fernández et al., 2017) that relies on country-specific commodity terms of trade indices based on international commodity prices. More precisely, we capture terms-of-trade shocks with the change in the natural logarithm of the commodity terms of trade index in Gruss (2014), which provides an estimate of the changes in disposable income, relative to GDP, arising from fluctuations in commodity prices:

where P_c,t is the logarithm of the real price (that is, in US dollars and divided by the IMF’s unit value index for manufactured exports) of commodity c in period t, with c = 1, …,46; and ∆ denotes first differences.

The weight of commodity c in country i, Ω_i,c,t in equation (5), is time varying. An alternative approach is to use average trade flows over a few years to construct country-specific commodity price indices (e.g., Aghion et al., 2010; Ricci et al., 2013). One reason for using time-invariant weights is to ensure that the movement in the index is invariant to changes in import and export volumes in response to commodity price fluctuations. A drawback, however, is that the mix of traded commodities and the overall importance of net commodity exports in output changes significantly over time. The index we employ here uses time-varying weights to capture these changes, but the weights are lagged to address endogeneity concerns.¹¹ More precisely, the weight of commodity c in country i for all monthly observations t within year τ is given by:

where x_i,c,τ (m_i,c,τ) denotes the exports (imports) value of commodity c of country i in year τ, expressed in US dollars; and GDP_i,τ denotes country i’s nominal GDP is US dollars in year τ. A one percentage point change in the commodity terms of trade index can thus be interpreted as a change in aggregate disposable income equivalent to one percentage point of GDP—providing a convenient cross-country normalization of the income effect associated with terms-of-trade shocks.

For ease of interpretation, variations in ctot have been reversed, so that a positive change denotes a deterioration in the terms of trade. Figure 6 shows the distribution of commodity terms-of-trade shocks for the estimation sample. The distributions for both advanced and emerging economies are very similar, centered around zero, and with a standard deviation of slightly less than half percentage point.

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Distribution of Commodity Terms-of-Trade Shocks

Citation: IMF Working Papers 2018, 280; 10.5089/9781484388846.001.A001

Source: Authors’ calculations.Note: The standard deviation for advanced (emerging) economies is 0.48 (0.44). The figure excludes observations below/above the 1^st/99^th percentile.

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How do terms-of-trade shocks affect domestic consumer prices? Commodity terms of trade can affect domestic consumer prices through two channels, and their impact depends on whether the exchange rate can adjust. Consider, first, that the exchange rate does not adjust. The first channel is the direct effect from the change in international commodity prices on the domestic price of consumer goods. The effect through this channel is however ambiguous. An increase in the price of a given commodity, which would have a direct positive effect on consumer prices, can cause the commodity terms of trade to increase or decrease, depending on whether the country is a net exporter or net importer of that commodity. The direct effect also depends on the weight of that specific commodity in the consumption basket, which could be very low in some cases (e.g., for some metals).

The second channel is indirect and due to the income effect from the terms-of-trade shock. The direction of the effect is unambiguous. A negative terms-of-trade shock, for instance, would lead to a decline in aggregate disposable income. This, in turn, would imply subdued aggregate demand and put downward pressure on domestic consumer prices.

If the exchange rate can adjust, there would be an additional and important propagation mechanism. A deterioration in the commodity terms of trade, with a consequent negative income effect, would trigger a depreciation of the domestic currency. Regardless of the direct effect associated with the change in international prices (i.e., in US dollars) that moved the terms of trade, the exchange rate depreciation triggered by the shock would have an unambiguous inflationary impact on consumer prices expressed in domestic currency.

In the analysis that follows, we thus condition the responses on the exchange rate regime and focus on the effect of anchoring within floats (i.e., under relatively flexible exchange rate regimes) where this channel is present.¹² We want to assess whether the inflationary effect of a negative shock to the terms of trade that triggers a depreciation of the domestic currency is smaller and fades out quicker when inflation expectations are better anchored. To test this hypothesis we explore whether the cumulative response of consumer prices after a terms-of-trade shock depends on how well anchored inflation expectations were before the shock hit.

3.2 Empirical Approach and Main Results

We estimate the cumulative response of the consumer price index over 12 months to a change in the country-specific commodity terms of trade index in a panel setting using the local projection method of Jordá (2005). A key advantage of this approach is that it can easily accommodate non-linearities in the impulse response functions and handle potential cross-country correlation in the error term (Auerbach and Gorodnichenko, 2012). Our baseline specification is as follows:

where p_i,t denotes the natural logarithm of the consumer price level in country i in period t;¹³ μ_i are country fixed effects; v_t are time fixed effects; ∆ denotes first difference; and ε_i,t+h is a random disturbance. anchor is the average value of the inflation expectations anchoring index described in section 2.3 over a rolling window that covers the preceding six years. flex is a dummy variable that takes a value of zero for fixed exchange rate regimes and a value of one otherwise, based on the exchange rate regime index of Ilzetzki et al. (2017).¹⁴ We include 12 lags of the change in consumer prices (i.e., J = 12).¹⁵

The specification in (7) is estimated by ordinary least squares for each h = 1,…, 12 using data for 31 economies at monthly frequency over 1999m1–2017m12.¹⁶ Since the dependent variable is defined in cumulative terms—it measures the cumulative growth in prices between t — 1 and t+h— the estimate of β^h is the cumulative impact of an innovation in the terms of trade on the CPI. Following Jorda et al. (2015), we use country-based cluster-robust standard errors to correct for potential serial correlation and heteroscedasticity.¹⁷

We argued before in favor of conditioning on the exchange rate regime and focusing on flexible arrangements since the transmission of terms-of-trade shocks to consumer prices differs depending on whether the exchange rate can react to the shock or not. So before studying the influence of anchoring on inflation persistence for floats, we first explore whether shocks to the terms of trade have a significant effect on consumer prices for flexible exchange rate regimes. To facilitate the interpretation of the results, it is useful to compute the conditional cumulative effect of a change in dot on the CPI: ¹⁸

Figure 7 shows the cumulative effect of a negative terms-of-trade shock for pegs (flex = 0) and floats (flex = 1) on CPI, with anchor evaluated at its average across countries and periods in the estimation sample. The results indicate that, indeed, a negative terms-of-trade shock leads to a significant increase in consumer prices in economies with flexible exchange rate regimes. Compared to the path of CPI in the absence of shocks, the price level increases steadily over the following 12 months. Instead, the response of consumer prices for pegs is statistically indistinguishable from zero.

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Response of Consumer Prices to a Terms-of-Trade Shock, by Exchange Rate Regime

Citation: IMF Working Papers 2018, 280; 10.5089/9781484388846.001.A001

Source: Authors’ calculations.Note: The figure shows the cumulative response of consumer prices to a negative terms-of-trade shock of 1 percent. The response of flexible (fixed) exchange rate corresponds to ${\hat{\beta }}_3^h+{\hat{\beta }}_4^h+{\hat{\beta }}_5^h\times \overline{anchor}+{\hat{\beta }}_6^h\times \overline{anchor}({\hat{\beta }}_3^h+{\hat{\beta }}_5^h\times \overline{anchor})$ in equation (8), where $\overline{anchor}$ denotes the average of the anchoring index in the estimation sample. Shaded areas denote 95 percent confidence intervals computed with country-based cluster-robust standard errors.

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Among floats, however, there is substantial variability in how well anchored inflation expectations are. Figure 8 shows that this is indeed the case both over the whole estimation sample (1998–2017, panel [a]) and over the more recent past (2012–17, panel b). Thus, we next turn to the main hypothesis we want to test: is the effect of a negative shock to the terms of trade on consumer price inflation less persistent when expectations are better anchored?

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Distribution of Anchoring Index among Floats

Citation: IMF Working Papers 2018, 280; 10.5089/9781484388846.001.A001

Source: Authors’ calculations.Note: Floats corresponds to observations with coarse classifications of 3 and 4 in Ilzetzki et al. (2017). The standard deviations of anchoring in panel (a) is 0.68 and 0.27 in panel (b).

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We start by exploring the response of the level of prices. Figure 9, panel (a), shows the cumulative response of the CPI for floats over 12 months following a negative terms-of-trade shock when: (i) expectations are strongly anchored (anchor = 75^th percentile of its sample distribution); and (ii) expectations are weakly anchored (anchor = 25^th percentile of its sample distribution). The results indicate that when inflation expectations are poorly anchored, a deterioration in the terms of trade associated with a drop in disposable income of one percent of GDP leads to a significant and persistent increase in consumer prices. The CPI increases by 0.35 percentage point after six months and 0.55 percentage point one year after the shock. Instead, when inflation expectations are strongly anchored, the cumulative response of consumer prices is indistinguishable from zero. The difference between the responses under weakly and strongly anchored expectations is statistically significant at the 95 percent confidence level (Figure 9, panel [b]).

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Response of Consumer Prices to a Terms-of-Trade Shock, by Anchoring

Citation: IMF Working Papers 2018, 280; 10.5089/9781484388846.001.A001

Source: Authors’ calculations.Note: The figures show the cumulative response of consumer prices to a negative terms-of-trade shock of 1 percent when the exchange rate regime is flexible. The response under strongly (weakly) anchored expectations in panel (a) corresponds to ${\hat{\beta }}_3^h+{\hat{\beta }}_4^h+{\hat{\beta }}_5^h\times ancho{r}_{p75}+{\hat{\beta }}_6^h\times ancho{r}_{p75}({\hat{\beta }}_3^h+{\hat{\beta }}_4^h+{\hat{\beta }}_5^h\times ancho{r}_{p25}+{\hat{\beta }}_6^h\times ancho{r}_{p25})$ in equation (8), where anchor_p75 (anchor_p25) denotes the 75th (25th) percentile of the anchoring index in the estimation sample. Shaded areas denote 95 percent confidence intervals computed with country-based cluster-robust standard errors.

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Figure 10 provides an alternative way to visualize our result, focusing on the cumulative response after 6 months for different degrees of anchoring. The solid grey line in panel (a) summarizes the marginal effect for floats of a negative shock to the commodity terms of trade at different values of the anchoring index. The dashed grey lines denote the 95 percent confidence interval. The black line shows the estimated kernel density of the anchoring index (i.e., distribution of anchoring) in the estimation sample. While the marginal effect at the 25^th percentile of anchoring is about 0.38 percent, it is much higher, about 0.93 percent, at the 10^th percentile of anchoring—that is, when the anchoring index is around -0.75. At the other extreme of the distribution the marginal effect is negative (e.g., it is [-0.17] percent at the 95^th percentile). This probably reflects that, for those economies, the effect on prices from weaker domestic demand as a result of the negative income effect predominates.

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Marginal Effect on Consumer Prices after 6 Months, by Anchoring

Citation: IMF Working Papers 2018, 280; 10.5089/9781484388846.001.A001

Source: Authors’ calculations.Note: The figure shows the marginal effect after six months of a negative terms-of-trade shock of 1 percent on consumer prices when the exchange rate regime is flexible. The chart reports results for levels of anchoring greater or equal than -0.83.

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We then explore the implications of anchoring for the persistence of the inflation rate. To this end, we estimate equation (7) but redefining the dependent variable as the month-on-month inflation rate (that is, ∆p_i,t+h-1 for h = 1, …, 12) annualized, rather than the cumulative change in the price level. The results are reported in Figure 11.¹⁹ The inflation rate increases by about 1.10 percentage points three months after the shock when inflation expectations are poorly anchored. Moreover, the reaction of inflation is very persistent: on average, the month-on-month inflation rate remains more than 0.60 percentage point above its pre-shock level even 12 months after the shock.

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Response of Inflation to a Terms-of-Trade Shock, by Anchoring

Citation: IMF Working Papers 2018, 280; 10.5089/9781484388846.001.A001

Source: Authors’ calculations.Note: The figures show the cumulative response of consumer price inflation to a negative terms-of-trade shock of 1 percent when the exchange rate regime is flexible. The response under strongly (weakly) anchored expectations in panel (a) corresponds to ${\hat{\beta }}_3^h+{\hat{\beta }}_4^h+{\hat{\beta }}_5^h\times ancho{r}_{p75}+{\hat{\beta }}_6^h\times ancho{r}_{p75}({\hat{\beta }}_3^h+{\hat{\beta }}_4^h+{\hat{\beta }}_5^h\times ancho{r}_{p25}+{\hat{\beta }}_6^h\times ancho{r}_{p25})$ in equation (8), where anchor_p75 (anchor _p25) denotes the 75th (25th) percentile of the anchoring index in the estimation sample. Shaded areas denote 95 percent confidence intervals computed with country-based cluster-robust standard errors.

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Inflation increases somewhat under anchored expectations—the response after two months is about 0.32 percentage points and statistically significant at the 95 percent confidence level. This is to be expected if the currency depreciation triggers an adjustment in relative prices and there is some downward rigidity in nominal prices. But when expectations are strongly anchored, the inflation rate returns quickly to its pre-shock level: the response of inflation is already not statistically different from zero three months after the shock.

3.3 Exchange Rate Depreciation and Pass-Through

These results suggest that the persistence of inflationary shocks is indeed larger when inflation expectation are poorly anchored. Given that the shock we are considering, a terms-of-trade shock, affects consumer prices primarily through the response of the exchange rate (as shown in Figure 7), a natural follow up question is whether the higher inflation persistence when expectations are poorly anchored is due to a larger currency depreciation, or to a larger exchange rate pass-through.

To answer this question, we explore whether the response of the exchange rate to a shock to the terms of trade is significantly different for economies with strongly and weakly anchored inflation expectations. We estimate the model in equation (7) but substituting consumer prices (p_it) with the natural logarithm of, alternatively, the nominal bilateral exchange rate (in local currency per U.S. dollar) and the import-weighted nominal effective exchange rate (as in Gopinath, 2015; and Carriére-Swallow et al., 2016).²⁰ The latter is given by:

where e_i,t is the natural logarithm of country i’s bilateral exchange rate (expressed in local currency per U.S. dollar, so that an increase denotes a depreciation of the domestic currency); ∆ is the first difference operator; and ω_ij,t is the share of exports from country j to country i in country i’s total imports as reported in the IMF’s Direction of Trade Statistics, lagged one year, and measured at annual frequency.

The results using the nominal exchange rate indicate that the magnitude of the depreciation following terms-of-trade shocks is not significantly related to the extent of anchoring. Figure 12 shows the cumulative response of the exchange rate up to 12 months for floats after a negative terms-of-trade shock when inflation expectations are strongly anchored (anchor = 75^th percentile of the sample distribution) and weakly anchored (anchor = 25^th percentile). The response of the exchange rate is somewhat larger for weakly-anchored countries than for countries with well anchored expectations, although the difference is generally not statistically significant. Figure 14, panel (a), focuses on the cumulative response after 6 months and shows that the marginal effect of a negative shock to the commodity terms of trade does not differ significantly for different values of the anchoring index.

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Response of the Nominal Exchange Rate to a Terms-of-Trade Shock, by Anchoring

Citation: IMF Working Papers 2018, 280; 10.5089/9781484388846.001.A001

Source: Authors’ calculations.Note: The figures show the cumulative response of the nominal exchange rate to a negative terms-of-trade shock of 1 percent when the exchange rate regime is flexible. The response under strongly (weakly) anchored expectations in panel (a) corresponds to ${\hat{\beta }}_3^h+{\hat{\beta }}_4^h+{\hat{\beta }}_5^h\times ancho{r}_{p75}+{\hat{\beta }}_6^h\times ancho{r}_{p75}({\hat{\beta }}_3^h+{\hat{\beta }}_4^h+{\hat{\beta }}_5^h\times ancho{r}_{p25}+{\hat{\beta }}_6^h\times ancho{r}_{p25})$ in equation (8), where anchor_p75 (anchor _p25) denotes the 75th(25th) percentile of the anchoring index in the estimation sample. Shaded areas denote 95 percent confidence intervals computed with country-based cluster-robust standard errors.

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Response of the Nominal Effective Exchange Rate to a Terms-of-Trade Shock, by Anchoring

Citation: IMF Working Papers 2018, 280; 10.5089/9781484388846.001.A001

Source: Authors’ calculations.Note: The figures show the cumulative response of the nominal effective exchange rate to a negative terms-of-trade shock of 1 percent when the exchange rate regime is flexible. The response under strongly (weakly) anchored expectations in panel (a) corresponds to ${\hat{\beta }}_3^h+{\hat{\beta }}_4^h+{\hat{\beta }}_5^h\times ancho{r}_{p75}+{\hat{\beta }}_6^h\times ancho{r}_{p75}({\hat{\beta }}_3^h+{\hat{\beta }}_4^h+{\hat{\beta }}_5^h\times ancho{r}_{p25}+{\hat{\beta }}_6^h\times ancho{r}_{p25})$ in equation (8), where anchor_p75 (anchor_p25) denotes the 75th (25th) percentile of the anchoring index in the estimation sample. Shaded areas denote 95 percent confidence intervals computed with country-based cluster-robust standard errors.

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Marginal Effect on the Nominal Exchange Rate after 6 Months, by Anchoring

Citation: IMF Working Papers 2018, 280; 10.5089/9781484388846.001.A001

Source: Authors’ calculations.Note: The figures show the marginal effect after six months of a negative terms-of-trade shock of 1 percent on the nominal exchange rate when the exchange rate regime is flexible. The charts report results for levels of anchoring greater or equal than -0.83.

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The results using the nominal effective exchange rate suggest that the depreciation may also be somewhat larger when expectations are poorly anchored (Figure 13 and Figure 14, panel [b]). But, again, the difference is only statistically significant for a few horizons.

The weak significance of the marginal effect of anchoring on the exchange rate response, together with the strong significance for consumer prices, suggest that two things are at play. When inflation expectations are poorly anchored, the exchange rate appears to depreciate by more in response to a given deterioration in the terms of trade. But, in addition, the pass-through rate from a given currency depreciation triggered by a terms-of-trade shock seems to be larger when inflation expectations are poorly anchored.²¹

3.4 Robustness

In this section we present a set of robustness tests to our main findings. In Figure 15 we show the estimated differences between the response of the CPI based on equation (7) when inflation expectations are strongly and weakly anchored. The baseline results are reported in panel (a) for convenience.

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Robustness Exercises—Response of Consumer Prices

Citation: IMF Working Papers 2018, 280; 10.5089/9781484388846.001.A001

Source: Authors’ calculations.Note: The figures show the difference in the cumulative response of consumer prices to a negative terms-of-trade shock of 1 percent when the exchange rate regime is flexible under strongly and weakly anchored expectations (which correspond to the 75^th and the 25^th percentile, respectively, of the anchoring index in the estimation sample). Shaded areas denote 95 percent confidence intervals computed with country-based cluster-robust standard errors.

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Panel (b) and (c) show the results under different exchange rate classifications. Panel (b) is still based on Ilzetzki et al. (2017), but we include observations of free falling exchange rates—that in most classifications are lumped together with ordinary flexible exchange rate regimes although they correspond to regimes with very high inflation (over 40 percent per year). Panel (c), instead, uses the updated version of the exchange rate classification of Shambaugh (2004). The results are very similar to those in the baseline exercise.

In panel (d) we report the results when the standard errors are corrected using the Driscoll and Kraay (1998) procedure—rather than clustering by country—which has the advantage that it takes cross-sectional dependence into account. The confidence intervals are wider under this alternative. But we can still reject the null that the responses of consumer prices under strongly and weakly anchored expectations are equal with a 95 percent confidence level.

One potential concern is that although the anchoring index is predetermined at the time of the shock (i.e., it is computed over the preceding six years), Metric #4—which captures the sensitivity of long-term expectations to inflation surprises—could be higher (i.e., reflect poor anchoring) if inflation is inherently more persistent. However, the robustness exercise reported in panel (e) shows that our main result holds when we exclude Metric #4 from the anchoring index.

Finally, our baseline analysis uses the anchoring index based on three-year ahead inflation expectations. The results in panel (f) shows that our main result holds when we use, instead, five-year ahead inflation expectations.